Question

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B and C. Show that the locus of the centroid of the triangle ABC is x^-2 + y^-2 + z^-2 = p^-2

Answer 1

Let equation of variable plane having directions cosines l, m, n which have a constant distance 3p from origin is 

lx + my + nz = 3p ... (1) 

Plane (1) cuts x-axis at A, where y = z = 0